VACCINATION AND RISK — and how this relates to masking

In a conversation about the current outbreaks of measles, someone just expressed confidence about their “3% risk, because they’re vaccinated”. And, they seem unconcerned about others opting-out. Let’s examine the mechanics of this — and the morals.

This 3% figure is roughly correct per exposure because the MMR vaccine is about 97% effective. But it’s important not to confuse “risk per exposure” with “actual risk.”

Your real-world risk is:

(Risk if exposed) × (Probability of being exposed)

And, probability of being exposed is dependent on community vaccination rates. Measles has an R0 of 12–18, meaning one infected person infects 12–18 others in an unvaccinated population.

Herd immunity threshold is around 95% — which means if you have less than 95% of the population vaccinated you won’t fully arrest the spread of it. If the vaccination rate is high (95% and up), circulating virus is rare, exposure probability approaches zero, and actual risk is negligible.

When vaccination rates drop: outbreaks occur, exposure probability skyrockets, and even vaccinated people face meaningful risk because they’re encountering the virus repeatedly. By the time you have 5 exposures, your probability of becoming a breakthrough case becomes 14.1%. At 10 exposures, your risk is 26.3% — more than a 1-in-4 chance.

Your personal protection degrades as others opt out — not because the vaccine weakens, but because you’re exposed more often.

The Independence Fallacy

There’s no such thing as epidemiological independence with communicable disease. The “independent choice” framework treats vaccination like seatbelt use — a personal risk decision. But infectious disease doesn’t work that way. YOUR choice directly modifies the risk environment for everyone else, and theirs modifies yours.

The Moral Problem

Some people cannot be vaccinated: infants under 12 months, immunocompromised individuals, people with specific allergies. They depend entirely on the rest of the population maintaining herd immunity. The “independent choice” position is essentially saying “I’ll free-ride on others’ vaccination while reserving my right not to contribute” — which only works if most people aren’t stupid and/or sociopathic.

Maths and Morals

The maths and morals of all this are very similar for masking: A certain percentage of airborne infections (e.g. COVID) will sneak past a defensively-worn mask, causing death or disability, even though the person was trying to defend against it. This is the same kind of risk-per-exposure math. The more people who refuse to mask, the greater the rate of exposures that can become that “sneak through” case. Widespread use of protective masking — those that arrest the spread at the face of the infected person — can lower exposure to near zero, making the entire society safer — including infants, CHF patients, dental patients, etc who actually cannot mask.